CN106655258A - Optimal load shedding method based on large power loss of secondary-constraint secondary-programming power system - Google Patents
Optimal load shedding method based on large power loss of secondary-constraint secondary-programming power system Download PDFInfo
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- CN106655258A CN106655258A CN201611006844.2A CN201611006844A CN106655258A CN 106655258 A CN106655258 A CN 106655258A CN 201611006844 A CN201611006844 A CN 201611006844A CN 106655258 A CN106655258 A CN 106655258A
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- 238000000034 method Methods 0.000 title claims abstract description 36
- 230000004888 barrier function Effects 0.000 claims description 11
- 230000009977 dual effect Effects 0.000 claims description 9
- 239000013598 vector Substances 0.000 claims description 9
- 238000010248 power generation Methods 0.000 abstract description 5
- 230000008901 benefit Effects 0.000 abstract description 3
- 238000010521 absorption reaction Methods 0.000 abstract 1
- 239000011159 matrix material Substances 0.000 description 6
- 239000000243 solution Substances 0.000 description 6
- 230000029087 digestion Effects 0.000 description 4
- 238000004364 calculation method Methods 0.000 description 3
- 230000005611 electricity Effects 0.000 description 3
- 238000002347 injection Methods 0.000 description 3
- 239000007924 injection Substances 0.000 description 3
- 230000002969 morbid Effects 0.000 description 3
- 238000012804 iterative process Methods 0.000 description 2
- 230000008569 process Effects 0.000 description 2
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- 230000008859 change Effects 0.000 description 1
- 230000000295 complement effect Effects 0.000 description 1
- 230000000694 effects Effects 0.000 description 1
- 230000008030 elimination Effects 0.000 description 1
- 238000003379 elimination reaction Methods 0.000 description 1
- 238000005516 engineering process Methods 0.000 description 1
- 230000007774 longterm Effects 0.000 description 1
- 238000005457 optimization Methods 0.000 description 1
- 230000010355 oscillation Effects 0.000 description 1
- 230000009467 reduction Effects 0.000 description 1
- 230000009466 transformation Effects 0.000 description 1
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Classifications
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- H02J3/383—
-
- H—ELECTRICITY
- H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
- H02J—CIRCUIT ARRANGEMENTS OR SYSTEMS FOR SUPPLYING OR DISTRIBUTING ELECTRIC POWER; SYSTEMS FOR STORING ELECTRIC ENERGY
- H02J3/00—Circuit arrangements for ac mains or ac distribution networks
- H02J3/12—Circuit arrangements for ac mains or ac distribution networks for adjusting voltage in ac networks by changing a characteristic of the network load
- H02J3/14—Circuit arrangements for ac mains or ac distribution networks for adjusting voltage in ac networks by changing a characteristic of the network load by switching loads on to, or off from, network, e.g. progressively balanced loading
-
- H—ELECTRICITY
- H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
- H02J—CIRCUIT ARRANGEMENTS OR SYSTEMS FOR SUPPLYING OR DISTRIBUTING ELECTRIC POWER; SYSTEMS FOR STORING ELECTRIC ENERGY
- H02J2203/00—Indexing scheme relating to details of circuit arrangements for AC mains or AC distribution networks
- H02J2203/20—Simulating, e g planning, reliability check, modelling or computer assisted design [CAD]
-
- Y—GENERAL TAGGING OF NEW TECHNOLOGICAL DEVELOPMENTS; GENERAL TAGGING OF CROSS-SECTIONAL TECHNOLOGIES SPANNING OVER SEVERAL SECTIONS OF THE IPC; TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
- Y02—TECHNOLOGIES OR APPLICATIONS FOR MITIGATION OR ADAPTATION AGAINST CLIMATE CHANGE
- Y02B—CLIMATE CHANGE MITIGATION TECHNOLOGIES RELATED TO BUILDINGS, e.g. HOUSING, HOUSE APPLIANCES OR RELATED END-USER APPLICATIONS
- Y02B70/00—Technologies for an efficient end-user side electric power management and consumption
- Y02B70/30—Systems integrating technologies related to power network operation and communication or information technologies for improving the carbon footprint of the management of residential or tertiary loads, i.e. smart grids as climate change mitigation technology in the buildings sector, including also the last stages of power distribution and the control, monitoring or operating management systems at local level
- Y02B70/3225—Demand response systems, e.g. load shedding, peak shaving
-
- Y—GENERAL TAGGING OF NEW TECHNOLOGICAL DEVELOPMENTS; GENERAL TAGGING OF CROSS-SECTIONAL TECHNOLOGIES SPANNING OVER SEVERAL SECTIONS OF THE IPC; TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
- Y02—TECHNOLOGIES OR APPLICATIONS FOR MITIGATION OR ADAPTATION AGAINST CLIMATE CHANGE
- Y02E—REDUCTION OF GREENHOUSE GAS [GHG] EMISSIONS, RELATED TO ENERGY GENERATION, TRANSMISSION OR DISTRIBUTION
- Y02E10/00—Energy generation through renewable energy sources
- Y02E10/50—Photovoltaic [PV] energy
- Y02E10/56—Power conversion systems, e.g. maximum power point trackers
-
- Y—GENERAL TAGGING OF NEW TECHNOLOGICAL DEVELOPMENTS; GENERAL TAGGING OF CROSS-SECTIONAL TECHNOLOGIES SPANNING OVER SEVERAL SECTIONS OF THE IPC; TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
- Y04—INFORMATION OR COMMUNICATION TECHNOLOGIES HAVING AN IMPACT ON OTHER TECHNOLOGY AREAS
- Y04S—SYSTEMS INTEGRATING TECHNOLOGIES RELATED TO POWER NETWORK OPERATION, COMMUNICATION OR INFORMATION TECHNOLOGIES FOR IMPROVING THE ELECTRICAL POWER GENERATION, TRANSMISSION, DISTRIBUTION, MANAGEMENT OR USAGE, i.e. SMART GRIDS
- Y04S20/00—Management or operation of end-user stationary applications or the last stages of power distribution; Controlling, monitoring or operating thereof
- Y04S20/20—End-user application control systems
- Y04S20/222—Demand response systems, e.g. load shedding, peak shaving
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- Engineering & Computer Science (AREA)
- Power Engineering (AREA)
- Supply And Distribution Of Alternating Current (AREA)
Abstract
The invention relates to an optimal load shedding method based on large power loss of a secondary-constraint secondary-programming power system. The method comprises the following steps that (1) a nonlinear programming model is established; (2) the model is optimized; and (3) a nonlinear programming primal-dual interior point method is used for solution. The method has the advantages that under the constraint that safe, stable, economical and high-efficiency operation of the power grid is ensured, the maximal installed capacity, that can be absorbed by the power distribution network, of distributed photovoltaic power generation is solved, factors that limits distributed photovoltaic power generation in the power distribution network are considered comprehensively, the absorption capability for distributed new energy of the power distribution network is analyzed, and the method has great significance in guiding ordered distributed photovoltaic access.
Description
Technical field
The invention belongs to power source planning field, especially a kind of power system based on quadratically constrained quadratic programming is high-power
Lose optimum cutting load method.
Background technology
It is grid-connected to distributed power source at aspects such as voltage deviation, voltage stability, harmonic pollution, relay protections both at home and abroad
Impact expand research, and propose corresponding solution.But the distributed new digestion capability researched and proposed
The measure of appraisal procedure and raising distributed new access capacity is all based on improving a certain item index of electrical network, not enough entirely
Face.Distributed photovoltaic digestion capability is assessed and referred under the constraint for ensureing the operation of electricity net safety stable economical and efficient, asks for distribution
The net distributed photovoltaic power generation to be dissolved maximum installed capacity.Consider in power distribution network restrict distributed photovoltaic power generation because
Element, analyzes power distribution network to the digestion capability of distributed new for the orderly access for instructing distributed photovoltaic has important meaning
Justice.
The content of the invention
The invention solves the problems that the shortcoming of above-mentioned prior art, there is provided a kind of computational efficiency is higher, more accurately based on secondary
The power system of constraint quadratic programming is high-power to lose optimum cutting load method.
The present invention solves the technical scheme that its technical problem is adopted：This power system based on quadratically constrained quadratic programming
High-power to lose optimum cutting load method, step is as follows：
(1) Nonlinear programming Model is set up
min f(X)
hi(X)=0 (i=1,2 ..., m)
gj(X) >=0 (j=1,2 ..., l) (1)
Wherein：X is decision variable vector；F (X) is object function；hi(X) it is equality constraints functions；gj(X) it is inequality
Constraint function；
(2) Optimized model
The Optimized model of distribution distributed energy access ultimate algorithm is as follows：
Obj.max.f(x) (2)
S.T.h (x)=0 (3)
(3) solved using Non-Linear Programming prim al- dual interior point m ethod
Introduce slack variable and functional inequality constraint is turned into equality constraint and variable inequality constraints；Taken advantage of with Lagrange
Sub- method processes equality constraint, and with interior barrier function method and restriction step length variable inequality constraints condition is processed；Derive
Ku En-Tu Ke the optimality conditions after barrier function are introduced, and is solved with Newton-Raphson approach；Take it is sufficiently large just
Feasibility of the beginning obstruction factor to ensure to solve, the optimality for being then gradually reduced obstruction factor to ensure to solve.
The invention has the advantages that：The method of the present invention is ensureing the constraint of electricity net safety stable economical and efficient operation
Under, the power distribution network distributed photovoltaic power generation to be dissolved maximum installed capacity is asked for, consider restriction distribution in power distribution network
The factor of formula photovoltaic generation, analyzes digestion capability of the power distribution network to distributed new, for instructing having for distributed photovoltaic
Sequence accesses significant.
Specific embodiment
Below the invention will be further described：
This power system based on quadratically constrained quadratic programming is high-power to lose optimum cutting load method, and step is as follows：
(1) Nonlinear programming Model is set up
For a Nonlinear programming Model comprising m equality constraint with l constraints, formula (1) can be used
Expression：
min f(X)
hi(X)=0 (i=1,2 ..., m) (1)
gj(X) >=0 (j=1,2 ..., l)
Wherein：X is decision variable vector；F (X) is object function；hi(X) it is equality constraints functions；gj(X) it is inequality
Constraint function；
(2) Optimized model
The Optimized model of distribution distributed energy access ultimate algorithm is as follows：
Obj.max.f(x) (2)
S.T.h (x)=0 (3)
Formula (2) is object function, is had：
Wherein, i is node serial number, and S is the node serial number collection for being conditionally accessible distributed energy, variableRepresent node i
The active of the distributed power source of upper access is exerted oneself.Using the object function, the target function value that can cause optimum results is equal to
The power-carrying that distribution distributed energy is accessed, it is ensured that the optimality of optimum results.
Formula (3) is equality constraint, i.e. node power equilibrium equation：
Wherein SPFor non-zero injection node (including PV node and PQ nodes) the numbering collection of active balance constraint, SQFor non-zero
Injection PQ node serial number collection, SZIt is zero injection node serial number collection；Pij(V, θ) and Qij(V, θ) is node power equation, is had：
Pij(V, θ)=ViVj(Gij cosθij+Bij sinθij) (9)
Qij(V, θ)=ViVj(Gij sinθij+Bij cosθij) (10)
The constraint of this group ensure that optimum results meet the basic physical rules of Operation of Electric Systems, it is ensured that understanding it is feasible
Property.
Formula (4) for power grid security economical operation a series of equality constraints, including but not limited to：
A branch roads current capacity is constrained
In operation of power networks, the trend of any appliance shall not exceed its long-term current-carrying capacity, i.e.,
B main transformers direction of tide is constrained
In operation of power networks, traffic department is not intended to distribution change it is generally desirable to the local load of distributed energy on-site elimination
Electricity
Generation power of standing send, therefore introduces constraint
Pij≤0 (12)
Wherein PijFor the active power that main transformer low-pressure side is conveyed to high-pressure side.
The active constraint of c sections
In operation of power networks, traffic department typically can be controlled to section effective power flow, to ensure certain reliability water
It is flat,
I.e.
The non-PV node voltage bound inequality constraints of d：
(3) solved using Non-Linear Programming prim al- dual interior point m ethod
Distributed power source access ultimate calculation optimization model has substantial amounts of inequality constraints condition, the place of inequality constraints
Reason is the key for affecting algorithm success or failure.In Non-Linear Programming field, current method mainly has active constraint collection strategy, exterior point to penalize
Function method, Multiplier punitive function method and interior barrier function method (also known as interior point method) etc..Active constraint collection strategy is along with constraint
Into and exit actively collection, required amount of calculation is generally large.Exterior point penalty function method easily causes Hai Sen when penalty factor increases
The excessive morbid state of Matrix condition number.Penalty factor is constant in Multiplier punitive function method, can avoid above-mentioned morbid state, but process
Easily occur alternately violating phenomenon when formula constraint is numerous.Interior point method achieves in recent years greatly progress, can avoid Hessian matrix
Morbid state, compared with active constraint collection strategy, amount of calculation is little, simple and easy to do, can in advance work before to boundary, anti-to cross the border in not
So, convergence is typically preferable.Using the newest research results of Non-Linear Programming interior point method, this project is right using Non-Linear Programming original
Even interior point method is solved.
Interior point method requires that iterative process is cheated to be carried out eventually inside feasible zone.Its basic thought is exactly taken at initial point feasible
Inside domain, and arrange together " obstacle " on the border of feasible zone, make iteration point near feasible zone border when, the target letter for being given
Numerical value increases rapidly, and suitable control step-length in an iterative process, so that iteration point is stayed in all the time inside feasible zone.Obviously,
With the reduction of obstruction factor, the effect of barrier function will be gradually lowered, and algorithmic statement is in the minimax solution of former problem.
Since Karmarkar proposes the interior-point algohnhm to linear programming with polynomial-time complexity, interior point method
The extensive concern of scholars is caused, and achieves greatly progress.Wherein, based on point in the former antithesis of logarithmic barrier function
Method receives extensive concern, and is successfully applied to the solution of power system quadratic programming and nonlinear programming problem.
Prim al- dual interior point m ethod is actually improved one kind of conventional interior point method.Its basic ideas is：Introduce slack variable
Functional inequality constraint is turned into equality constraint and variable inequality constraints；Equality constraint bar is processed with method of Lagrange multipliers
Part, with interior barrier function method and restriction step length variable inequality constraints condition is processed；Derive and introduce the storehouse after barrier function
En-Tu Ke optimality conditions, and solved with Newton-Raphson approach；Take the sufficiently large initial obstacle factor to ensure solution
Feasibility, be then gradually reduced obstruction factor with ensure solve optimality.
First, it is considered to following nonlinear programming problem：
min f(x) (15)
S.t.h (x)=0 (16)
Wherein x is n-dimensional vector；H is m dimensional vectors；G is r dimensional vectors.
Introduce slack variable inequality constraints is turned into equality constraint and variable inequality constraints, will formula (17) be changed to：
For the inequality constraints condition in formula (18), barrier function item is introduced, then had：
Wherein p is obstruction factor, and p>0；Subscript i represents i-th element of vector.
It is as follows according to formula (16), formula (18) and formula (19) definable Lagrangian：
Wherein x, l and u are original variable vector；Y, z and w be corresponding Lagrange multiplier vector, i.e., dual variable to
Amount.
Thus Kuhn and Tooke condition (to write conveniently, replacing F (x, y, l, u, z, w) with F below) can be derived：
l,u,w>0, z ＜ 0 (27)
Wherein L, U, Z and W are respectively the diagonal matrix constituted as diagonal element with vectorial l, u, z and w each element；E is that r dimensions are complete
One is vectorial, i.e. e=[1,1 ... 1]T；Formula (25) and formula (21) are complementary slackness condition.
Formula (16) to formula (22) uses Newton-Raphson approach iterative, can obtain update equation as follows：
Wherein
OrderThen have
Wherein H ' is revised Hessian matrix；J is the Jacobian matrix of equality constraint.NoteThen V is
To extend Hessian matrix.
For variable inequality constraints l, u, w>0, z ＜ 0, suitably chooses initial value, then in each iteration using system
About step length come ensure solve interior property.I.e.：
Wherein, TPAnd TDThe amendment step-length of former variable and dual variable is represented respectively.
Prim al- dual interior point m ethod is typically based on duality gap to determine obstruction factor, i.e.,
Wherein σ be centripetal parameter, its span for (0,1]；R is inequality constraints number；CgapFor duality gap, i.e.,
Prim al- dual interior point m ethod typically takes a fully big initial obstacle factor when starting, and as σ ∈, (0, when 1), algorithm will
A certain optimal solution is gradually converged on p → 0.The value of σ is the key factor of the performance for affecting algorithm.When σ takes higher value
When, algorithm mainly considers the feasibility for solving, and numerical stability is typically preferable, but convergence rate may be slower；When σ takes smaller value
When, algorithm mainly considers the optimality for solving, and convergence rate is typically very fast, but numerical stability is poor, easily causes vibration, makes
Convergence of algorithm speed slows down, or even oscillation and divergence.In practicality, when σ takes 0.01 to 0.2, algorithm typically can obtain preferable receipts
Holding back property.
In prim al- dual interior point m ethod, the introducing of slack variable eliminates functional inequality constraint, therefore only need to be to slack variable
And corresponding Lagrange multiplier provides appropriate initial value, you can ensure interior property of initial solution, without carrying out for this
Special calculating.
In addition to the implementation, the present invention can also have other embodiment.All employing equivalents or equivalent transformation shape
Into technical scheme, all fall within the protection domain of application claims.
Claims (1)
1. a kind of power system based on quadratically constrained quadratic programming is high-power loses optimum cutting load method, it is characterized in that：Step
It is rapid as follows：
(1) Nonlinear programming Model is set up
min f(X)
hi(X)=0 (i=1,2 ..., m) (1)
gj(X) >=0 (j=1,2 ..., l)
Wherein：X is decision variable vector；F (X) is object function；hi(X) it is equality constraints functions；gj(X) it is inequality constraints
Function；
(2) Optimized model
The Optimized model of distribution distributed energy access ultimate algorithm is as follows：
Obj. max.f(x) (2)
S.T. h (x)=0 (3)
(3) solved using Non-Linear Programming prim al- dual interior point m ethod
Introduce slack variable and functional inequality constraint is turned into equality constraint and variable inequality constraints；Use method of Lagrange multipliers
Equality constraint is processed, with interior barrier function method and restriction step length variable inequality constraints condition is processed；Derive and introduce
Ku En-Tu Ke optimality conditions after barrier function, and solved with Newton-Raphson approach；Take sufficiently large initial barrier
The feasibility for hindering the factor to ensure to solve, the optimality for being then gradually reduced obstruction factor to ensure to solve.
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Citations (2)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN105514992A (en) * | 2015-12-11 | 2016-04-20 | 国家电网公司 | Grid-structure photovoltaic consumption capability optimization method based on trend constraints |
| CN105762832A (en) * | 2015-12-25 | 2016-07-13 | 国家电网公司 | Distribution network distributed energy access limit optimization method |
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- 2016-11-16 CN CN201611006844.2A patent/CN106655258A/en active Pending
Patent Citations (2)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN105514992A (en) * | 2015-12-11 | 2016-04-20 | 国家电网公司 | Grid-structure photovoltaic consumption capability optimization method based on trend constraints |
| CN105762832A (en) * | 2015-12-25 | 2016-07-13 | 国家电网公司 | Distribution network distributed energy access limit optimization method |
Non-Patent Citations (1)
| Title |
|---|
| 王俊: ""电力系统实时紧急控制的研究"", 《中国优秀硕士学位论文全文数据库 工程科技II辑（2005年第06期）》 * |
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